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Mathematics - Algebra | Linear Algebra

Linear Algebra

Petersen, Peter

2012, X, 390 p.

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  • Contains considerably more material on differential equations, as examples and as motivation, than is typical in a linear algebra textbook
  • Includes an excellent selection of good exercises
  • Classroom tested for an upper undergraduate course in linear algebra
This textbook on linear algebra includes the key topics of the subject that most advanced undergraduates need to learn before entering graduate school. All the usual topics, such as complex vector spaces, complex inner products, the Spectral theorem for normal operators, dual spaces, the minimal polynomial, the Jordan canonical form, and the rational canonical form, are covered, along with a chapter on determinants at the end of the book. In addition, there is material throughout the text on linear differential equations and how it integrates with all of the important concepts in linear algebra.
 
This book has several distinguishing features that set it apart from other linear algebra texts.  For example: Gaussian elimination is used as the key tool in getting at eigenvalues; it takes an essentially determinant-free approach to linear algebra; and systems of linear differential equations are used as frequent motivation for the reader.  Another motivating aspect of the book is the excellent and engaging exercises that abound in this text.
 
This textbook is written for an upper-division undergraduate course on Linear Algebra.  The prerequisites for this book are a familiarity with basic matrix algebra and elementary calculus, although any student who is willing to think abstractly should not have too much difficulty in understanding this text.

Content Level » Lower undergraduate

Keywords » Gaussian elimination - Jordan canonical form - characteristic polynomial - complex inner products - dual spaces - eigenvalues - linear algebra - linear differential equations - linear maps - linear operators - minimal polynomial - spectral theorem - vector spaces

Related subjects » Algebra

Table of contents 

Preface.- 1 Basic Theory.- 2 Linear Operators.- 3 Inner Product Spaces.- 4 Linear Operators on Inner Product Spaces.- 5 Determinants.- Bibliography.- Index

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